Bogolyubov approximation for diagonal model of an interacting Bose gas

We study, using the Bogolyubov approximation, the thermodynamic behaviour of a superstable Bose system whose energy operator in the second-quantized form contains a nonlinear expression in the occupation numbers operators. We prove that for all values of the chemical potential satisfying $\mu > \lambda(0)$, where $\lambda (0)\leq 0$ is the lowest energy value, the system undergoes Bose--Einstein condensation

Soluble model of Bose-atoms with two level internal structure: non-conventional Bose-Einstein condensation

For a Bose atom system whose energy operator is diagonal in the so-called number operators and its ground state has an internal two-level structure with negative energies, exact expressions for the limit free canonical energy and pressure are obtained. The existence of non-conventional Bose-Einstein condensation has been also proved.Для системи Бозе-атомів, чий оператор енергії є діагональним за так званим числом операторів і його основний стан має внутрішню дворівневу структуру з негативними енергіями, одержано точні вирази для граничних вільної канонічної енергії та тиску. Доведено існування нестандартної Бозе - Айнштайнівської конденсації

Coexistence of Non-Conventional Condensates in Two-Level Bose Atom System

In the framework of the Bogolyubov approximation and using the Bogolyubov inequalities we give a simple proof of the coexistence of two non-conventional Bose-Einstein condensates in the case of some superstable Bose system whose atoms have an internal two-level structure and their energy operators in the second quantized form depend on the number operators only.Comment: 17 page

Soluble model of Bose-atoms with two level internal structure: non-conventional Bose-Einstein condensation

For a Bose atom system whose energy operator is diagonal in the so-called number operators and its ground state has an internal two-level structure with negative energies, exact expressions for the limit free canonical energy and pressure are obtained. The existence of non-conventional Bose-Einstein condensation has been also proved